František Kardoš
Published 2014-09-08Version 1
Fullerene graphs, i.e., 3-connected planar cubic graphs with pentagonal and hexagonal faces, are conjectured to be hamiltonian. This is a special case of a conjecture of Barnette, dating back to the 60s, stating that 3-connected planar graphs with faces of size at most 6 are hamiltonian. We prove the conjecture.
Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture
Planar cubic graphs of small diameter
On Barnette's Conjecture and $H^{+-}$ property
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